Priors don’t update. That’s why they’re called “priors”.
Marginal posterior probabilities update; this is learning. Inductive priors over sequences don’t update; they are what does the updating, they define your capability to learn. Even if you are a self-modifying AI and can rewrite your own source code, from a Bayesian perspective this is simply folded into an inductive prior over sequences of observations. I previously tried to write a post on this topic, but it got way too long and is now in my backlog of essays to finish someday.
This is exactly what I was trying to get at by distinguishing between the statement, “The marginal probability of drawing a red ball on the third round is 50%”, which is true in all three scenarios above; versus the prior distributions over sequences of observations, which are different.
The inductive prior defines your responses to sequences of observations. This does not change over time; it is outside time. Learning how to learn is simply folded into the joint probability distribution.
Priors don’t update. That’s why they’re called “priors”.
John shows up on time for meetings 30%.
John has been reprimanded.
I think there is 95% chance he will be on time for meetings from now on.
You could just say that 95% is my prior for P(OnTime|Reprimanded), but I am not sure people think this way; “prior has been updated” seems more appropriate (when the condition is history).
Priors don’t update. That’s why they’re called “priors”.
Marginal posterior probabilities update; this is learning. Inductive priors over sequences don’t update; they are what does the updating, they define your capability to learn. Even if you are a self-modifying AI and can rewrite your own source code, from a Bayesian perspective this is simply folded into an inductive prior over sequences of observations. I previously tried to write a post on this topic, but it got way too long and is now in my backlog of essays to finish someday.
This is exactly what I was trying to get at by distinguishing between the statement, “The marginal probability of drawing a red ball on the third round is 50%”, which is true in all three scenarios above; versus the prior distributions over sequences of observations, which are different.
The inductive prior defines your responses to sequences of observations. This does not change over time; it is outside time. Learning how to learn is simply folded into the joint probability distribution.
John shows up on time for meetings 30%.
John has been reprimanded.
I think there is 95% chance he will be on time for meetings from now on.
You could just say that 95% is my prior for P(OnTime|Reprimanded), but I am not sure people think this way; “prior has been updated” seems more appropriate (when the condition is history).
Just call it your “current belief”.